If you are on foot, then you can simply stroll down to Main street to do some shopping or eating or take a walk down the pier. You can also cross the street and stroll down the beach in either direction.

As for "attractions" within walking distance your choices are limited to the surf museum downtown. I am not sure if that will work for you and your baby.

If you plan to take a trip to Catalina, your options are a cab or bus ride to Balboa (Newport Beach) or Long Beach. Newport is probably more convenient but the shuttle from there takes one trip in the morning and one at night so be prepared to stay all day. The shuttle from long beach leaves (pretty much) every hour throughout the day. The aquarium is a must if you are going to long beach. Agressively you could do both the aquarium and Catalina in one day.

Check out the hb public library story times at the main street branch. Its within walking distance of your hotel and provides an awesome fun filled story time with other tots and moms. I think its wed mornings at 10am? Shipley nature center also has some kid stuff. Ask the hb moms groups for better info. And of course theres always D-Land / California Adventure...

Let's add Adventure Playground by the HB Library too!

(its a Huck Finn type of playgound..mud included) Minimal charge to get in. :)